1413:«Considerantes nostre civitatis et civium honorem atque profectum, qui eis, tam per doctrinam quam per sedula obsequia discreti et sapientis viri magistri Leonardi Bigolli, in abbacandis estimationibus et rationibus civitatis eiusque officialium et aliis quoties expedit, conferuntur; ut eidem Leonardo, merito dilectionis et gratie, atque scientie sue prerogativa, in recompensationem laboris sui quem substinet in audiendis et consolidandis estimationibus et rationibus supradictis, a Comuni et camerariis publicis, de Comuni et pro Comuni, mercede sive salario suo, annis singulis, libre xx denariorum et amisceria consueta dari debeant (ipseque pisano Comuni et eius officialibus in abbacatione de cetero more solito serviat), presenti constitutione firmamus». F. Bonaini,
428:
44:
1300:
he said: "Having been introduced there to this art with an amazing method of teaching by means of the nine figures of the
Indians, I loved the knowledge of such an art to such an extent above all other arts and so much did I devote myself to it with my intellect, that I learned with very earnest
540:
In the
Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next
1301:
application and through the technique of contradiction anything to be studied concerning it and its various methods used in Egypt, in Syria, in Greece, in Sicily, and in
Provence, places I have later visited for the purpose of commerce" (translated by G. Germano,
500:, and methods to convert numbers to it. The second section explains uses in business, for example converting different currencies, and calculating profit and interest, which were important to the growing banking industry. The book also discusses
477:, converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. Replacing Roman numerals, its
407:
honored
Fibonacci (referred to as Leonardo Bigollo) by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens.
1373:), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.
527:
posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as
1962:
368:
coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which, unlike the
2202:
1138:
496:
The original 1202 manuscript is not known to exist. In a 1228 copy of the manuscript, the first section introduces the numeral system and compares it with others, such as
443:
showing (in box on right) the
Fibonacci sequence with the position in the sequence labeled with Latin numbers and Roman numerals and the value in Hindu-Arabic numerals
1362:
The basic meanings of "bigollo" appear to be "bilingual" or "traveller". A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of
537:
contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century.
1549:
1990:
2167:
1941:
779:
166:
1781:
1723:
932:
357:, in modern-day Algeria. Fibonacci travelled with him as a young boy, and it was in Bugia (Algeria) where he was educated that he learned about the
1616:
909:
2197:
2091:
1979:
1584:
161:
1392:
2162:
1717:
1687:
1266:
1124:
1069:
307:
992:
2117:
2112:
2107:
689:
565:
316:('son of Bonacci'). However, even earlier, in 1506, a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci".
1803:
1482:
1272:
807:
2036:
1834:
1190:
1075:
440:
1839:
1444:
878:
661:
569:
1879:
1897:
1514:
1476:
1438:
1024:
851:
1957:"Fibonacci, Leonardo, or Leonardo of Pisa." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. (April 20, 2015).
2177:
653:
396:
1360:
by David
Singmaster, 18 March 2004 – emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."
1114:
462:
358:
320:
145:
1366:
1309:
1238:
478:
857:
353:
Fibonacci was born around 1170 to
Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in
1355:
1747:
2192:
1541:
2172:
1198:
923:
573:
2187:
2182:
2122:
2006:
1910:
1167:
485:
for calculations, was an advance in making business calculations easier and faster, which assisted the growth of
775:
1984:
553:
In the 19th century, a statue of
Fibonacci was set in Pisa. Today it is located in the western gallery of the
2029:
889:
1707:
918:
554:
2157:
2009:
1612:
906:
1574:
2152:
1709:
The Art of
Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4
1384:
675:
649:
2128:
2068:
1974:
1970:
1921:
1579:
645:
558:
470:
1042:
Finding
Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World
2086:
2022:
2001:
1608:
988:
501:
373:
49:
1679:
1219:
954:
403:, posed several questions based on Arab mathematical works for Fibonacci to solve. In 1240, the
1893:
1875:
1797:
1713:
1683:
1510:
1472:
1466:
1434:
1262:
1256:
1215:
1130:
1120:
1065:
1020:
847:
801:
640:
1187:
1059:
473:. The book showed the practical use and value of this by applying the numerals to commercial
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1650:
1428:
694:
528:
517:
427:
404:
336:
292:
266:
241:
235:
191:
156:
72:
20:
1751:
1370:
1313:
1242:
1194:
959:
913:
699:
400:
1868:
1672:
893:
585:
581:
497:
369:
24:
1958:
2146:
1655:
1638:
928:
577:
505:
365:
288:
122:
1363:
1306:
1235:
1890:
The Origins of Value: The Financial Innovations That Created Modern Capital Markets
1096:
1037:
843:
542:
354:
837:
2060:
1771:
1012:
833:
615:
599:
474:
434:
422:
379:
326:
296:
137:
1917:
1210:
Singh, Parmanand. "Acharya Hemachandra and the (so called) Fibonacci Numbers".
43:
1055:
490:
1744:
1134:
604:(1202), a book on calculations (English translation by Laurence Sigler, 2002)
611:
1159:
1575:"The Man of Numbers: Fibonacci's Arithmetic Revolution [Excerpt]"
657:
627:
399:, who enjoyed mathematics and science. A member of Frederick II's court,
285:
151:
1351:
839:
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
568:
because of a connection to the Fibonacci numbers. Examples include the
486:
1536:
1534:
883:
752:
is "good-natured", so the full name means "son from a good-natured ".
623:
482:
1061:
Great Calculations: A Surprising Look Behind 50 Scientific Inquiries
1905:
1417:, «Giornale storico degli archivi toscani» 1, 4, 1857, pp. 239–246.
545:
as the limit of the ratio of consecutive numbers in this sequence.
295:, considered to be "the most talented Western mathematician of the
580:. Beyond mathematics, namesakes of Fibonacci include the asteroid
458:
426:
411:
Fibonacci is thought to have died between 1240 and 1250, in Pisa.
323:
in the Western world primarily through his composition in 1202 of
1415:
Memoria unica sincrona di Leonardo Fibonacci, novamente scoperta
619:
466:
68:
2018:
1796:
Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857).
1639:"The so-called fibonacci numbers in ancient and medieval India"
1357:
Sources in Recreational Mathematics: An Annotated Bibliography
250:
218:
215:
2014:
1509:, translated by Sigler, Laurence E., Springer-Verlag, 2002,
1775:
1258:
Medieval Science, Technology, and Medicine: An Encyclopedia
221:
206:
636:(1225), solutions to problems posed by Johannes of Palermo
1802:. Tip. delle Scienze Fisiche e Matematiche. p. 231.
630:(English translation by Barnabas Hughes, Springer, 2008).
200:
1913:
International Center for Finance Working Paper No. 03–28
541:
place, the value 377. Fibonacci did not speak about the
48:
Statue of Fibonacci (1863) by Giovanni Paganucci in the
1888:
Goetzmann, William N. and Rouwenhorst, K.Geert (2005).
1255:
Thomas F. Glick; Steven Livesey; Faith Wallis (2014).
1101:
The Man of Numbers: Fibonacci's Arithmetic Revolution,
800:
Smith, David Eugene; Karpinski, Louis Charles (1911),
392:), which popularized Hindu–Arabic numerals in Europe.
306:, was made up in 1838 by the Franco-Italian historian
1870:
The Man of Numbers: Fibonacci's Arithmetic Revolution
1827:"The Man of Numbers: In Search of Leonardo Fibonacci"
1303:
New editorial perspectives in Fibonacci's Liber abaci
1232:
New editorial perspectives in Fibonacci's Liber abaci
247:
244:
212:
197:
194:
806:, Boston and London: Ginn and Company, p. 128,
253:
203:
2100:
2079:
2052:
372:used at the time, allowed easy calculation using a
209:
175:
128:
118:
98:
79:
56:
34:
1867:
1671:
1924:, Vol. 11, No. 1, February 1973, pp. 99–104.
1188:Leonardo Pisano: "Contributions to number theory"
842:(First trade paperback ed.). New York City:
335:) and also introduced Europe to the sequence of
1776:"Sequence A000045 (Fibonacci Numbers)"
1201:Online, 2006. p. 3. Retrieved 18 September 2006.
1568:
1566:
2030:
1501:
1499:
1430:Fibonacci and Lucas Numbers with Applications
1017:An Introduction to the History of Mathematics
8:
1927:Horadam, A. F. "Eight hundred years young,"
1935:
718:Fibonacci's actual appearance is not known.
597:
532:
522:
453:(1202), Fibonacci introduced the so-called
448:
432:
377:
340:
324:
311:
135:
2037:
2023:
2015:
1113:Drozdyuk, Andriy; Drozdyuk, Denys (2010).
42:
31:
2203:Court of Frederick II, Holy Roman Emperor
1782:On-Line Encyclopedia of Integer Sequences
1654:
1044:. Princeton University Press. p. 24.
770:
768:
2092:Greedy algorithm for Egyptian fractions
1980:MacTutor History of Mathematics Archive
982:
980:
978:
828:
826:
824:
764:
711:
1906:Fibonacci and the Financial Revolution
1603:
1601:
1395:from the original on 17 September 2016
1116:Fibonacci, his numbers and his rabbits
610:(1220), a compendium of techniques in
23:. For the Prison Break character, see
1934:Gavin, J., Schärlig, A., extracts of
1892:. Oxford University Press Inc., US,
1331:Leonardo Pisano's book of calculation
739:('Leonardo the Traveller from Pisa').
265:
7:
2118:Generalizations of Fibonacci numbers
2113:List of things named after Fibonacci
2108:Fibonacci numbers in popular culture
1991:Fibonacci (2 vol., 1857 & 1862)
1918:The Autobiography of Leonardo Pisano
1678:. Indiana University Press. p.
1542:"Fibonacci: The Man Behind The Math"
1471:, Infobase Publishing, p. 192,
1433:, John Wiley & Sons, p. 3,
690:Fibonacci numbers in popular culture
16:Italian mathematician (c. 1170–1245)
2168:13th-century Italian mathematicians
1835:Mathematical Association of America
1119:. Toronto: Choven Pub. p. 18.
1929:The Australian Mathematics Teacher
1806:from the original on 13 March 2023
1305:, «Reti medievali rivista» 14, 2,
1234:, «Reti medievali rivista» 14, 2,
1078:from the original on 13 March 2023
14:
1333:, New York, Springer-Verlag, 2003
935:from the original on 12 June 2012
339:, which he used as an example in
1383:Keith Devlin (7 November 2002).
1214:. Ed. Siwan, 20(1):28–30, 1986.
1064:. Prometheus Books. p. 35.
991:. www-history.mcs.st-and.ac.uk.
670:(on commercial arithmetic; lost)
626:, and other topics in practical
302:The name he is commonly called,
240:
190:
1845:from the original on 2015-09-07
1726:from the original on 2023-03-13
1619:from the original on 2015-08-23
1587:from the original on 2014-06-18
1552:from the original on 2011-07-16
1485:from the original on 2023-03-13
1447:from the original on 2023-03-13
1275:from the original on 2023-03-13
1170:from the original on 2019-10-13
1141:from the original on 2020-02-17
995:from the original on 2019-10-28
860:from the original on 2023-03-13
810:from the original on 2023-03-13
782:from the original on 2014-02-22
479:ancient Egyptian multiplication
441:Biblioteca Nazionale di Firenze
364:Fibonacci travelled around the
2198:Italian expatriates in Algeria
1712:. Addison-Wesley. p. 50.
1670:Goonatilake, Susantha (1998).
1329:was published by L.E. Sigler,
960:Merriam-Webster.com Dictionary
662:Brahmagupta–Fibonacci identity
570:Brahmagupta–Fibonacci identity
566:concepts named after Fibonacci
465:, with ten digits including a
1:
2163:13th-century writers in Latin
2000:– digital facsimile from the
1465:Tanton, James Stuart (2005),
557:, historical cemetery on the
278:
271:
83:
60:
19:For the number sequence, see
1656:10.1016/0315-0860(85)90021-7
1613:"The Man Behind Modern Math"
776:"Fibonacci's Statue in Pisa"
564:There are many mathematical
376:. In 1202, he completed the
179:Guglielmo "Bonacci" (father)
1975:"Leonardo Pisano Fibonacci"
1745:Math for poets and drummers
1468:Encyclopédia of Mathematics
1364:"Eight hundred years young"
1325:The English edition of the
989:"Leonardo Pisano Fibonacci"
463:Hindu–Arabic numeral system
359:Hindu–Arabic numeral system
146:Hindu–Arabic numeral system
2219:
1772:Sloane, N. J. A.
1350:pisani..." (quoted in the
1261:. Routledge. p. 172.
1103:A&C Black, 2012 p. 13.
924:Collins English Dictionary
574:Fibonacci search technique
515:
420:
321:Indo–Arabic numeral system
319:Fibonacci popularized the
162:Fibonacci–Sylvester method
18:
2123:The Fibonacci Association
1911:Yale School of Management
1814:– via Google Books.
1346:: "Incipit flos Leonardi
803:The Hindu–Arabic Numerals
395:Fibonacci was a guest of
41:
1985:University of St Andrews
1799:Scritti: Il Liber Abbaci
1637:Singh, Pamanand (1985).
674:Commentary on Book X of
2178:Italian Roman Catholics
2007:Fibonacci, Liber abbaci
1940:online and analyzed on
1903:Goetzmann, William N.,
1674:Toward a Global Science
1507:Fibonacci's Liber Abaci
1199:Encyclopædia Britannica
890:Oxford University Press
737:Leonardo Bigollo Pisano
531:. Although Fibonacci's
390:The Book of Calculation
1936:
1866:Devlin, Keith (2012).
1825:Devlin, Keith (2010).
1706:Knuth, Donald (2006).
1427:Koshy, Thomas (2011),
598:
584:and the art rock band
533:
523:
461:), today known as the
449:
444:
433:
431:A page of Fibonacci's
378:
341:
325:
312:
136:
93:Pisa, Republic of Pisa
2010:Bibliotheca Augustana
1019:. Brooks Cole, 1990:
886:UK English Dictionary
879:"Fibonacci, Leonardo"
650:Diophantine equations
481:method, and using an
430:
267:[fiboˈnattʃi]
1971:Robertson, Edmund F.
1909:(October 23, 2003),
1694:Virahanka Fibonacci.
1643:Historia Mathematica
919:"Fibonacci sequence"
656:. See in particular
654:Emperor Frederick II
397:Emperor Frederick II
2129:Fibonacci Quarterly
2069:The Book of Squares
1997:Practica Geometriae
1969:O'Connor, John J.;
1922:Fibonacci Quarterly
1609:Gordon, John Steele
1580:Scientific American
1385:"A man to count on"
1342:See the incipit of
1164:www.halexandria.org
1160:"Fibonacci Numbers"
646:The Book of Squares
608:Practica Geometriae
559:Piazza dei Miracoli
471:positional notation
333:Book of Calculation
2193:Medieval geometers
2087:Fibonacci sequence
2002:Linda Hall Library
1931:31 (1975) 123–134.
1838:. pp. 21–28.
1785:. OEIS Foundation.
1750:2012-02-12 at the
1369:2008-12-19 at the
1312:2021-07-09 at the
1241:2021-07-09 at the
1193:2008-06-17 at the
1027:(6th ed.), p. 261.
955:"Fibonacci number"
912:2019-06-23 at the
907:"Fibonacci series"
846:. pp. 92–93.
512:Fibonacci sequence
502:irrational numbers
445:
374:place-value system
105:Leonardo Fibonacci
50:Camposanto di Pisa
2173:Fibonacci numbers
2140:
2139:
1947:
1719:978-0-321-33570-8
1689:978-0-253-33388-9
1268:978-1-135-45932-1
1126:978-0-9866300-1-9
1071:978-1-63388-029-0
963:. Merriam-Webster
778:. Epsilones.com.
748:The etymology of
676:Euclid's Elements
641:Liber quadratorum
618:and partition of
529:Fibonacci numbers
337:Fibonacci numbers
310:and is short for
232:
183:
182:
157:Fibonacci numbers
144:Popularizing the
90:(aged 79–80)
2210:
2188:People from Pisa
2183:Number theorists
2039:
2032:
2025:
2016:
1987:
1946:
1939:
1885:
1874:. Walker Books.
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1743:Hall, Rachel W.
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973:
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898:
897:
892:. Archived from
875:
869:
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866:
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830:
819:
817:
816:
815:
797:
791:
790:
788:
787:
772:
753:
746:
740:
733:Leonardo of Pisa
729:Leonardo Bonacci
725:
719:
716:
695:Republic of Pisa
603:
536:
526:
518:Fibonacci number
452:
438:
405:Republic of Pisa
383:
344:
330:
315:
293:Republic of Pisa
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167:Fibonacci method
141:
108:Leonardo Bonacci
99:Other names
89:
85:
73:Republic of Pisa
65:
62:
46:
32:
21:Fibonacci number
2218:
2217:
2213:
2212:
2211:
2209:
2208:
2207:
2143:
2142:
2141:
2136:
2096:
2075:
2048:
2043:
1968:
1954:
1916:Grimm, R. E., "
1882:
1865:
1862:
1860:Further reading
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1752:Wayback Machine
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1573:Devlin, Keith.
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1371:Wayback Machine
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1058:(7 July 2015).
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914:Wayback Machine
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726:
722:
717:
713:
708:
700:Adelard of Bath
686:
652:, dedicated to
594:
551:
520:
514:
457:(method of the
425:
419:
401:John of Palermo
351:
308:Guillaume Libri
281:
274:
262:
243:
234:
233:
193:
189:
171:
114:
111:Leonardo Pisano
94:
91:
87:
75:
66:
63:
52:
37:
28:
17:
12:
11:
5:
2216:
2214:
2206:
2205:
2200:
2195:
2190:
2185:
2180:
2175:
2170:
2165:
2160:
2155:
2145:
2144:
2138:
2137:
2135:
2134:
2133:
2132:
2120:
2115:
2110:
2104:
2102:
2098:
2097:
2095:
2094:
2089:
2083:
2081:
2077:
2076:
2074:
2073:
2065:
2056:
2054:
2050:
2049:
2044:
2042:
2041:
2034:
2027:
2019:
2013:
2012:
2004:
1993:Il liber abaci
1988:
1966:
1965:at Convergence
1960:
1953:
1952:External links
1950:
1949:
1948:
1932:
1925:
1914:
1901:
1886:
1881:978-0802779083
1880:
1861:
1858:
1856:
1855:
1817:
1788:
1763:
1736:
1718:
1698:
1688:
1662:
1649:(3): 229–244.
1629:
1597:
1562:
1530:
1521:
1515:
1495:
1477:
1457:
1439:
1419:
1406:
1375:
1335:
1318:
1285:
1267:
1247:
1223:
1203:
1180:
1151:
1125:
1105:
1089:
1070:
1047:
1029:
1005:
974:
946:
899:
896:on 2021-05-12.
870:
852:
844:Broadway Books
820:
792:
763:
761:
758:
755:
754:
741:
727:Also known as
720:
710:
709:
707:
704:
703:
702:
697:
692:
685:
682:
681:
680:
671:
668:Di minor guisa
665:
637:
631:
605:
593:
590:
586:The Fibonaccis
582:6765 Fibonacci
550:
547:
516:Main article:
513:
510:
498:Roman numerals
421:Main article:
418:
413:
386:Book of Abacus
370:Roman numerals
355:Bugia (Béjaïa)
350:
347:
313:filius Bonacci
282: 1240–50
181:
180:
177:
173:
172:
170:
169:
164:
159:
154:
149:
142:
132:
130:
129:Known for
126:
125:
120:
116:
115:
113:
112:
109:
106:
102:
100:
96:
95:
92:
81:
77:
76:
67:
58:
54:
53:
47:
39:
38:
35:
25:Otto Fibonacci
15:
13:
10:
9:
6:
4:
3:
2:
2215:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2150:
2148:
2131:
2130:
2126:
2125:
2124:
2121:
2119:
2116:
2114:
2111:
2109:
2106:
2105:
2103:
2099:
2093:
2090:
2088:
2085:
2084:
2082:
2078:
2071:
2070:
2066:
2063:
2062:
2058:
2057:
2055:
2051:
2047:
2040:
2035:
2033:
2028:
2026:
2021:
2020:
2017:
2011:
2008:
2005:
2003:
1999:
1998:
1994:
1989:
1986:
1982:
1981:
1976:
1972:
1967:
1964:
1961:
1959:
1956:
1955:
1951:
1945:
1944:
1938:
1933:
1930:
1926:
1923:
1919:
1915:
1912:
1908:
1907:
1902:
1899:
1898:0-19-517571-9
1895:
1891:
1887:
1883:
1877:
1872:
1871:
1864:
1863:
1859:
1841:
1837:
1836:
1828:
1821:
1818:
1805:
1801:
1800:
1792:
1789:
1784:
1783:
1777:
1773:
1767:
1764:
1761:(2008) 10–11.
1760:
1757:
1756:Math Horizons
1753:
1749:
1746:
1740:
1737:
1725:
1721:
1715:
1711:
1710:
1702:
1699:
1695:
1691:
1685:
1681:
1676:
1675:
1666:
1663:
1657:
1652:
1648:
1644:
1640:
1633:
1630:
1618:
1614:
1610:
1604:
1602:
1598:
1586:
1582:
1581:
1576:
1569:
1567:
1563:
1551:
1547:
1543:
1537:
1535:
1531:
1525:
1522:
1518:
1516:0-387-95419-8
1512:
1508:
1502:
1500:
1496:
1484:
1480:
1478:9780816051243
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1470:
1469:
1461:
1458:
1446:
1442:
1440:9781118031315
1436:
1432:
1431:
1423:
1420:
1416:
1410:
1407:
1394:
1390:
1386:
1379:
1376:
1372:
1368:
1365:
1359:
1358:
1353:
1349:
1345:
1339:
1336:
1332:
1328:
1322:
1319:
1315:
1311:
1308:
1304:
1299:
1295:
1289:
1286:
1274:
1270:
1264:
1260:
1259:
1251:
1248:
1244:
1240:
1237:
1233:
1227:
1224:
1221:
1217:
1213:
1207:
1204:
1200:
1196:
1192:
1189:
1184:
1181:
1169:
1165:
1161:
1155:
1152:
1140:
1136:
1132:
1128:
1122:
1118:
1117:
1109:
1106:
1102:
1098:
1093:
1090:
1077:
1073:
1067:
1063:
1062:
1057:
1051:
1048:
1043:
1039:
1038:Devlin, Keith
1033:
1030:
1026:
1025:0-03-029558-0
1022:
1018:
1014:
1009:
1006:
994:
990:
987:MacTutor, R.
983:
981:
979:
975:
962:
961:
956:
950:
947:
934:
930:
929:HarperCollins
926:
925:
920:
915:
911:
908:
903:
900:
895:
891:
887:
885:
880:
874:
871:
859:
855:
853:0-7679-0816-3
849:
845:
841:
840:
835:
829:
827:
825:
821:
809:
805:
804:
796:
793:
781:
777:
771:
769:
765:
759:
751:
745:
742:
738:
734:
730:
724:
721:
715:
712:
705:
701:
698:
696:
693:
691:
688:
687:
683:
678:
677:
672:
669:
666:
663:
659:
655:
651:
647:
643:
642:
638:
635:
632:
629:
625:
621:
617:
613:
609:
606:
602:
601:
596:
595:
591:
589:
587:
583:
579:
578:Pisano period
575:
571:
567:
562:
560:
556:
548:
546:
544:
538:
535:
530:
525:
519:
511:
509:
507:
506:prime numbers
503:
499:
494:
492:
488:
484:
480:
476:
472:
468:
464:
460:
456:
455:modus Indorum
451:
442:
437:
436:
429:
424:
417:
414:
412:
409:
406:
402:
398:
393:
391:
387:
382:
381:
375:
371:
367:
366:Mediterranean
362:
360:
356:
348:
346:
343:
338:
334:
329:
328:
322:
317:
314:
309:
305:
300:
298:
294:
290:
289:mathematician
287:
268:
258:
237:
226:
187:
178:
174:
168:
165:
163:
160:
158:
155:
153:
150:
147:
143:
140:
139:
134:
133:
131:
127:
124:
123:Mathematician
121:
117:
110:
107:
104:
103:
101:
97:
82:
78:
74:
70:
59:
55:
51:
45:
40:
33:
30:
26:
22:
2158:1170s births
2127:
2067:
2059:
2045:
1996:
1992:
1978:
1942:
1928:
1904:
1889:
1869:
1847:. Retrieved
1833:
1820:
1808:. Retrieved
1798:
1791:
1779:
1766:
1758:
1755:
1739:
1728:. Retrieved
1708:
1701:
1693:
1673:
1665:
1646:
1642:
1632:
1621:. Retrieved
1589:. Retrieved
1578:
1554:. Retrieved
1545:
1524:
1506:
1487:, retrieved
1467:
1460:
1449:, retrieved
1429:
1422:
1414:
1409:
1397:. Retrieved
1389:The Guardian
1388:
1378:
1356:
1347:
1343:
1338:
1330:
1327:Liber abacci
1326:
1321:
1302:
1298:Liber abacci
1297:
1293:
1288:
1277:. Retrieved
1257:
1250:
1231:
1230:G. Germano,
1226:
1211:
1206:
1183:
1172:. Retrieved
1163:
1154:
1143:. Retrieved
1115:
1108:
1100:
1097:Keith Devlin
1092:
1080:. Retrieved
1060:
1050:
1041:
1032:
1016:
1013:Eves, Howard
1008:
997:. Retrieved
965:. Retrieved
958:
949:
937:. Retrieved
922:
902:
894:the original
882:
873:
862:. Retrieved
838:
834:Livio, Mario
812:, retrieved
802:
795:
784:. Retrieved
749:
744:
736:
732:
728:
723:
714:
673:
667:
639:
633:
607:
563:
552:
543:golden ratio
539:
521:
495:
454:
446:
415:
410:
394:
389:
385:
363:
352:
332:
318:
303:
301:
185:
184:
88:(1250-00-00)
29:
2153:1250 deaths
2061:Liber Abaci
1937:Liber Abaci
1810:20 December
1307:pp. 157–173
1236:pp. 157–173
616:measurement
600:Liber Abaci
534:Liber Abaci
524:Liber Abaci
493:in Europe.
475:bookkeeping
450:Liber Abaci
435:Liber Abaci
423:Liber Abaci
416:Liber Abaci
380:Liber Abaci
342:Liber Abaci
327:Liber Abaci
297:Middle Ages
275: 1170
138:Liber Abaci
64: 1170
2147:Categories
1849:2018-12-21
1730:2020-11-11
1623:2015-08-28
1591:2015-08-29
1556:2015-08-29
1528:Grimm 1973
1489:2015-12-12
1451:2015-12-12
1279:2018-12-07
1174:2015-04-29
1145:2020-01-26
1082:19 January
1056:Colin Pask
999:2018-12-22
864:2018-12-19
814:2016-03-02
786:2010-08-02
760:References
576:, and the
555:Camposanto
491:accounting
119:Occupation
2046:Fibonacci
1963:Fibonacci
1354:document
1220:0047-6269
1135:813281753
836:(2003) .
612:surveying
439:from the
349:Biography
304:Fibonacci
291:from the
284:) was an
186:Fibonacci
148:in Europe
36:Fibonacci
2080:Theories
1840:Archived
1804:Archived
1748:Archived
1724:Archived
1617:Archived
1585:Archived
1550:Archived
1483:archived
1445:archived
1393:Archived
1367:Archived
1310:Archived
1294:Prologus
1273:Archived
1239:Archived
1191:Archived
1168:Archived
1139:Archived
1076:Archived
1040:(2017).
993:Archived
933:Archived
910:Archived
858:Archived
808:archived
780:Archived
684:See also
660:and the
658:congruum
628:geometry
263:Italian:
152:Congruum
2101:Related
1774:(ed.).
1546:NPR.org
1352:MS Word
1348:bigolli
1296:of the
1292:In the
967:23 June
939:23 June
750:Bonacci
624:volumes
487:banking
459:Indians
447:In the
286:Italian
2072:(1225)
2064:(1202)
1943:BibNum
1896:
1878:
1716:
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1475:
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1133:
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884:Lexico
850:
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614:, the
572:, the
549:Legacy
483:abacus
176:Parent
2053:Books
1843:(PDF)
1830:(PDF)
735:, or
706:Notes
620:areas
592:Works
1995:and
1894:ISBN
1876:ISBN
1812:2018
1780:The
1714:ISBN
1684:ISBN
1511:ISBN
1473:ISBN
1435:ISBN
1401:2016
1344:Flos
1263:ISBN
1216:ISSN
1212:Math
1131:OCLC
1121:ISBN
1084:2020
1066:ISBN
1021:ISBN
969:2019
941:2019
916:and
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634:Flos
622:and
504:and
489:and
469:and
467:zero
231:also
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